No-spill cup assemblies are well known in the art. In the past, a variety of such assemblies have been developed and marketed. In general, the goal of a no-spill cup is to provide a construction which minimizes or prevents liquid from emerging out of the cup when liquid flow is not desired, i.e. when the user is not drinking. However, though the assemblies of the prior art are intended to avoid such accidents, their construction is such that they generally do not provide a secure enough protection against undesirable spilling or leakage. Thus, when such cups are inverted, or more significantly, when they are shaken vigorously, liquid will often emerge from them. This can be a particular problem with young children, for whom these cups are usually intended. Accordingly, there is a need in the art for an improved cup assembly for preventing undesired spilling of liquids.